Exponent Rules: Review & Practice

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  • 0:00 What Are Powers in Math?
  • 0:47 Power Laws
  • 3:41 Formulas
  • 4:41 Lesson Summary
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Lesson Transcript
Instructor: Vanessa Botts
When working with exponents, it's important to understand power laws, which are also called laws of exponents. In this lesson, you'll learn about these laws, their formulas and when to use them.

What Are Powers in Math?

Powers, also called exponents, correspond to the number of times a base is used as a factor. For example, if you have a number n raised to the power of 3 (n^3), it means that the n is multiplied by itself three times. So, the exponent (3) says how many times to use the number (n) in a multiplication.

Of course, dealing with exponents isn't always as easy as multiplying a number three times. Sometimes there are combinations of exponents that need to be calculated, such as:

powerf

How do you solve this equation? Well, there are several rules governing different combinations of powers. These laws are called power laws, or rules of exponents, and knowing them can simplify many computations involving exponents.

Power Laws

There are actually quite a few exponent rules, but eight of them are more commonly used and those are the ones we'll explore in this lesson.

First up is the zero exponent rule. This rule is so simple, it's almost hard to believe. It does not matter how small or large the number is, if it is raised to the 0 power, the answer will always be 1. For example:

power2

Next is the exponent of 1 rule. This one's just as simple: Any number raised to the power of 1 will always remain the same.

power3

Now, to move on to something a bit more complicated: product rules. These are rules for multiplying terms with the same base and different exponents. For example:

power4

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